{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "生成训练测试数据集："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10000, 200)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import time\n",
    "\n",
    "m = 10000\n",
    "d = 200\n",
    "k = 50\n",
    "\n",
    "trains = np.zeros((m, d))\n",
    "for i in range(m):\n",
    "    trains[i] = np.array([random.gauss(0, 1) for z in range(d)])\n",
    "test = np.array([random.gauss(0, 1) for z in range(d)])\n",
    "\n",
    "print(trains.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python 实现 Annoy："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from queue import PriorityQueue\n",
    "\n",
    "def means(X):\n",
    "    \"\"\"\n",
    "    启发式的选取两个点\n",
    "\n",
    "    参数\n",
    "    ----------\n",
    "    X : 特征矩阵\n",
    "    \n",
    "    返回\n",
    "    ----------\n",
    "    两个向量点\n",
    "    \"\"\"\n",
    "    iteration_steps = 20\n",
    "    count = X.shape[0]\n",
    "    i = np.random.randint(0, count)\n",
    "    j = np.random.randint(0, count - 1)\n",
    "    # 保证 i\\j 不相同\n",
    "    j += (j >= i)\n",
    "    ic = 1\n",
    "    jc = 1\n",
    "    p = X[i]\n",
    "    q = X[j]\n",
    "    for l in range(iteration_steps):\n",
    "        k = np.random.randint(0, count)\n",
    "        di = ic * distance(p, X[k])\n",
    "        dj = jc * distance(q, X[k])\n",
    "        if di == dj:\n",
    "            continue\n",
    "        if di < dj:\n",
    "            p = (p * ic + X[k]) / (ic + 1)\n",
    "            ic = ic + 1\n",
    "        else:\n",
    "            q = (q * jc + X[k]) / (jc + 1)\n",
    "            jc = jc + 1\n",
    "    return p, q\n",
    "        \n",
    "def distance(a, b):\n",
    "    \"\"\"\n",
    "    计算距离\n",
    "\n",
    "    参数\n",
    "    ----------\n",
    "    a : 向量 a\n",
    "\n",
    "    b : 向量 b\n",
    "    \n",
    "    返回\n",
    "    ----------\n",
    "    向量 a 与 向量 b 直接的距离\n",
    "    \"\"\"\n",
    "    return np.linalg.norm(a - b)\n",
    "\n",
    "class annoynode:\n",
    "    \"\"\"\n",
    "    Annoy 树结点\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, index, size, w, b, left = None, right = None):\n",
    "        # 结点包含的样本点下标\n",
    "        self.index = index\n",
    "        # 结点及其子结点包含的样本数\n",
    "        self.size = size\n",
    "        # 分割超平面的系数\n",
    "        self.w = w\n",
    "        # 分割超平面的偏移量\n",
    "        self.b = b\n",
    "        # 左子树\n",
    "        self.left = left\n",
    "        # 右子树\n",
    "        self.right = right\n",
    "    \n",
    "    def __lt__(self, other):\n",
    "        # 结点大小比较\n",
    "        return self.size < other.size\n",
    "\n",
    "class annoytree:\n",
    "    \"\"\"\n",
    "    Annoy 树算法实现\n",
    "    \n",
    "    参数\n",
    "    ----------\n",
    "    X : 特征矩阵\n",
    "\n",
    "    leaf_size : 叶子节点包含的最大特征向量数量，默认为 10\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, X, leaf_size = 10):\n",
    "        def build_node(X_indexes):\n",
    "            \"\"\"\n",
    "            构建结点\n",
    "            \n",
    "            参数\n",
    "            ----------\n",
    "            X_indexes : 特征矩阵下标\n",
    "            \"\"\"\n",
    "            # 当特征矩阵小于等于指定的叶子结点的大小时，创建叶子结点并返回\n",
    "            if len(X_indexes) <= leaf_size:\n",
    "                return annoynode(X_indexes, len(X_indexes), None, None)\n",
    "            # 当前特征矩阵\n",
    "            _X = X[X_indexes, :]\n",
    "            # 启发式的选取两点\n",
    "            p, q = means(_X)\n",
    "            # 超平面的系数\n",
    "            w = p - q\n",
    "            # 超平面的偏移量\n",
    "            b = -np.dot((p + q) / 2, w)\n",
    "            # 构建结点\n",
    "            node = annoynode(None, len(X_indexes), w, b)\n",
    "            # 在超平面“左”侧的特征矩阵下标\n",
    "            left_index = (_X.dot(w) + b) > 0\n",
    "            if left_index.any():\n",
    "                # 递归的构建左子树\n",
    "                node.left = build_node(X_indexes[left_index])\n",
    "            # 在超平面“右”侧的特征矩阵下标\n",
    "            right_index = ~left_index\n",
    "            if right_index.any():\n",
    "                # 递归的构建右子树\n",
    "                node.right = build_node(X_indexes[right_index])\n",
    "            return node\n",
    "        # 根结点\n",
    "        self.root = build_node(np.array(range(X.shape[0])))\n",
    "        \n",
    "class annoytrees:\n",
    "    \"\"\"\n",
    "    Annoy 算法实现\n",
    "    \n",
    "    参数\n",
    "    ----------\n",
    "    X : 特征矩阵\n",
    "    \n",
    "    n_trees : Annoy 树的数量，默认为 10\n",
    "\n",
    "    leaf_size : 叶子节点包含的最大特征向量数量，默认为 10\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, X, n_trees = 10, leaf_size = 10):\n",
    "        self._X = X\n",
    "        self._trees = []\n",
    "        # 循环的创建 Annoy 树\n",
    "        for i in range(n_trees):\n",
    "            self._trees.append(annoytree(X, leaf_size = leaf_size))\n",
    "            \n",
    "    def query(self, x, k = 1, search_k = -1):\n",
    "        \"\"\"\n",
    "        查询距离最近 k 个特征向量\n",
    "\n",
    "        参数\n",
    "        ----------\n",
    "        x : 目标向量\n",
    "\n",
    "        k : 查询邻居数量\n",
    "\n",
    "        search_k : 最少遍历出的邻居数量，默认为 Annoy 树的数量 * 查询数量\n",
    "        \"\"\"\n",
    "        \n",
    "        # 创建结点优先级队列\n",
    "        nodes = PriorityQueue()\n",
    "        # 先将所有根结点加入到队列中\n",
    "        for tree in self._trees:\n",
    "            nodes.put([float(\"inf\"), tree.root])\n",
    "        if search_k == -1:\n",
    "            search_k = len(self._trees) * k\n",
    "        # 待查询的邻居下标数组\n",
    "        nns = []\n",
    "        # 循环优先级队列\n",
    "        while len(nns) < search_k and not nodes.empty():\n",
    "            # 获取优先级最高的结点\n",
    "            (dist, node) = nodes.get()\n",
    "            # 如果是叶子结点，将下标数组加入待查询的邻居中\n",
    "            if node.left is None and node.right is None:\n",
    "                nns.extend(node.index)\n",
    "            else:\n",
    "                # 计算目标向量到结点超平面的距离\n",
    "                dist = min(dist, np.abs(x.dot(node.w) + node.b))\n",
    "                # 将距离做为优先级的结点加入到优先级队列中\n",
    "                if node.left is not None:\n",
    "                    nodes.put([dist, node.left])\n",
    "                if node.right is not None:\n",
    "                    nodes.put([dist, node.right])\n",
    "        # 对下标数组进行排序\n",
    "        nns.sort()\n",
    "        prev = -1\n",
    "        # 优先级队列\n",
    "        nns_distance = PriorityQueue()\n",
    "        for idx in nns:\n",
    "            # 过滤重复的特征矩阵下标\n",
    "            if idx == prev:\n",
    "                continue\n",
    "            prev = idx\n",
    "            # 计算特征向量与目标向量的距离做为优先级\n",
    "            nns_distance.put([distance(x, self._X[idx]), idx])\n",
    "        nearests = []\n",
    "        distances = []\n",
    "        # 取前 k 个\n",
    "        for i in range(k):\n",
    "            if nns_distance.empty():\n",
    "                break\n",
    "            (dist, idx) = nns_distance.get()\n",
    "            nearests.append(idx)\n",
    "            distances.append(dist)\n",
    "        return nearests, distances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Annoy 构建与查询："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Annoy Build:  0.17376995086669922\n",
      "Annoy Search:  0.0003261566162109375\n",
      "Indexes:  [2087 2955 2820 5860 4858 5183 3419 3120 8935  469 2795 6300 4401  220\n",
      " 2491  322 2130 4204 1069 7695 3611 7304 3229 3546 6951  948 2653 3541\n",
      " 8488 5504 2233 7134 5726 7599 8718 1936 4895 6350 4688 9304 2724 2305\n",
      " 4615 3241 7749 1851 1433  514 8820 2685]\n",
      "Distances:  [17.03445244 17.074543   17.23371887 17.29202843 17.3838768  17.38926888\n",
      " 17.39016724 17.42239571 17.43660164 17.43716049 17.44219589 17.46596336\n",
      " 17.46749687 17.48422623 17.49925041 17.50570679 17.5290432  17.58576202\n",
      " 17.58647156 17.59267235 17.59703255 17.61027718 17.6764679  17.67796135\n",
      " 17.69918251 17.71703529 17.7469635  17.77556801 17.77716064 17.79926109\n",
      " 17.80227661 17.80312729 17.81699371 17.83490944 17.87693596 17.88405037\n",
      " 17.88469887 17.88484573 17.90133476 17.91887474 17.92709732 17.9437542\n",
      " 17.96082115 17.97278595 17.98053169 17.98347473 18.00175476 18.0065403\n",
      " 18.01778221 18.0187149 ]\n"
     ]
    }
   ],
   "source": [
    "from annoy import AnnoyIndex\n",
    "\n",
    "start = time.time()\n",
    "# 初始化 AnnoyIndex，使用欧式距离\n",
    "t = AnnoyIndex(d, 'euclidean')\n",
    "for i in range(m):\n",
    "    # 添加样本点\n",
    "    t.add_item(i, trains[i])\n",
    "# 构建 20 棵二叉树\n",
    "t.build(20)\n",
    "cost = time.time() - start\n",
    "print(\"Annoy Build: \", cost)\n",
    "\n",
    "start = time.time()\n",
    "# 查询 test 点最近 k 个样本点\n",
    "nearests, distances = t.get_nns_by_vector(test, k, include_distances=True)\n",
    "cost = time.time() - start\n",
    "print(\"Annoy Search: \", cost)\n",
    "print(\"Indexes: \", np.array(nearests))\n",
    "print(\"Distances: \", np.array(distances))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ball Tree 构建与查询："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ball Tree Build:  0.07265377044677734\n",
      "Ball Tree Search:  0.003065824508666992\n",
      "Indexes:  [1982 8244 2150 2087 7455 5220 4507 7382 2955 2938 8253  269 1891 2820\n",
      " 2435 5860 2729 1767 9968 7977 3578 5488 5032  254 4858 5183 5107 3419\n",
      " 1034 5208  822 3120 7765 8935  469 2941 2795 2564 6300 5096 4401 1490\n",
      " 3919 6312 4282 6407  220 6676 6910 7415]\n",
      "Distances:  [16.89884757 16.96648838 17.01921737 17.03445208 17.04229582 17.04643241\n",
      " 17.05813518 17.07179647 17.07454464 17.12051775 17.14960123 17.18627548\n",
      " 17.22199311 17.23371743 17.24356866 17.29202753 17.30379704 17.30954783\n",
      " 17.31187673 17.32290499 17.32307655 17.36471041 17.37858653 17.38091254\n",
      " 17.38387616 17.3892679  17.39015788 17.39016637 17.40299881 17.41015991\n",
      " 17.4151256  17.42239582 17.42578051 17.43660148 17.43716072 17.4372148\n",
      " 17.44219691 17.46312689 17.46596197 17.46743996 17.46749663 17.46862695\n",
      " 17.46926795 17.47576712 17.47624183 17.47633038 17.48422532 17.48533048\n",
      " 17.48934812 17.49741322]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.neighbors import BallTree\n",
    "\n",
    "start = time.time()\n",
    "tree = BallTree(trains)\n",
    "cost = time.time() - start\n",
    "print(\"Ball Tree Build: \", cost)\n",
    "\n",
    "start = time.time()\n",
    "distances, nearests = tree.query(np.array([test]), k)\n",
    "cost = time.time() - start\n",
    "print(\"Ball Tree Search: \", cost)\n",
    "print(\"Indexes: \", nearests[0])\n",
    "print(\"Distances: \", distances[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "python 实现构建与查询："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Indexes:  [5220 2955 7977 5032 1034 7415 9406 4012 1069 8811 2081 3851 1936 4084\n",
      " 7668 1992  514 6796 4675 1916  517 4380 5446 6020 7681 4271 4878 9438\n",
      " 9095 8229  202 7945 6700 9719 5937 5313 3802 7043 2083  222 4437 6515\n",
      " 1430 3959 7935 9424 2671  866 5316 4408]\n",
      "Distances:  [17.04643241 17.07454464 17.32290499 17.37858653 17.40299881 17.49741322\n",
      " 17.5387657  17.54287361 17.58647167 17.61416024 17.65120569 17.83754937\n",
      " 17.88404998 17.92391482 17.98436859 18.00448112 18.00654011 18.02729789\n",
      " 18.04183201 18.06602622 18.09846612 18.10092578 18.13414213 18.13613252\n",
      " 18.15330249 18.1656789  18.17441276 18.1784536  18.17989569 18.20001631\n",
      " 18.20619473 18.23051494 18.24594438 18.26846985 18.27265548 18.27894962\n",
      " 18.28403095 18.3032248  18.30631446 18.31198453 18.3244178  18.32679832\n",
      " 18.33354389 18.35832998 18.36840283 18.36974737 18.37060299 18.38133618\n",
      " 18.38979675 18.39271755]\n"
     ]
    }
   ],
   "source": [
    "at = annoytrees(trains, 20)\n",
    "nearests, distances = at.query(test, k)\n",
    "print(\"Indexes: \", np.array(nearests))\n",
    "print(\"Distances: \", np.array(distances))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "平衡二叉树演示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
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       "            warnings.style.display = 'block';\n",
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       "                'This browser does not support binary websocket messages. ' +\n",
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       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
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       "\n",
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       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    var resizeObserver = new ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = 'image/png';\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data']);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.one(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "\n",
    "%matplotlib notebook\n",
    "\n",
    "def means_step(X, iteration_steps = 200):\n",
    "    count = X.shape[0]\n",
    "    i = np.random.randint(0, count)\n",
    "    j = np.random.randint(0, count - 1)\n",
    "    j += (j >= i)\n",
    "    ic = 1\n",
    "    jc = 1\n",
    "    p = X[i]\n",
    "    q = X[j]\n",
    "    ps = np.zeros((iteration_steps, len(p)))\n",
    "    qs = np.zeros((iteration_steps, len(q)))\n",
    "    ts = np.zeros((iteration_steps, len(q)))\n",
    "    for l in range(iteration_steps):\n",
    "        p, q, ic, jc, _ = step(X, p, q, ic, jc)\n",
    "        ps[l], qs[l], ts[l] = p, q, _\n",
    "    return ps, qs, ts\n",
    "\n",
    "def step(X, p, q, ic, jc):\n",
    "    k = np.random.randint(0, X.shape[0])\n",
    "    di = ic * distance(p, X[k])\n",
    "    dj = jc * distance(q, X[k])\n",
    "    if di == dj:\n",
    "        return\n",
    "    if di < dj:\n",
    "        p = (p * ic + X[k]) / (ic + 1)\n",
    "        ic = ic + 1\n",
    "    else:\n",
    "        q = (q * jc + X[k]) / (jc + 1)\n",
    "        jc = jc + 1\n",
    "    return p, q, ic, jc, X[k]\n",
    "\n",
    "plt.rcParams['font.sans-serif'] = ['PingFang HK']  # 选择一个本地的支持中文的字体\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_facecolor('#f8f9fa')\n",
    "\n",
    "np.random.seed(0)\n",
    "X = np.array([[1,1], [2,3], [3,-1], [0,0], [-1,-2], [-2, 2], [-4, 4], [3,-1], [1, -4],[0,2], [-3, 0]])\n",
    "itr = 50\n",
    "ps, qs, ts = means_step(X, iteration_steps = itr)\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "plt.xlim(x_min, x_max)\n",
    "plt.ylim(y_min, y_max)\n",
    "x1 = X[:, 0]\n",
    "y1 = X[:, 1]\n",
    "plt.scatter(x1, y1, c='#e63946', marker='.')\n",
    "\n",
    "p = plt.scatter(ps[0][0], ps[0][1], c='#457b9d', marker='$P$', s=60)\n",
    "q = plt.scatter(qs[0][0], qs[0][1], c='#457b9d', marker='$Q$', s=60)\n",
    "t = plt.scatter(ts[0][0], ts[0][1], c='#457b9d', marker='$T$', s=60)\n",
    "\n",
    "def update(i):\n",
    "    p.set_offsets(ps[i])\n",
    "    q.set_offsets(qs[i])\n",
    "    if i + 1 < itr:\n",
    "        t.set_offsets(ts[i + 1])\n",
    "    else:\n",
    "        t.set_offsets([10, 10])\n",
    "    return p, q, t\n",
    "\n",
    "ani = animation.FuncAnimation(fig, update, range(1, itr), interval=500, blit=True, repeat=False)\n",
    "ani.save('means.gif')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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